A survey of interval methods for differential equations

A brief introduction to the basic concepts, methods, and applications of interval analysis will be followed by a broad survey of interval methods for differential equations. We can obtain rigorous upper and lower bounds on sets of solutions corresponding to bounded sets of input data (initial values, boundary values, coefficients or parameters in the differential equations). The methods apply to nonlinear problems as well as linear ones. We will consider both ordinary and partial differential equations. This approach is not only more reliable and more rigorous than classical methods, but it is simpler as well. Uncertainty due to round-off error is taken into account automatically by the use of interval arithmetic with directed rounding.